Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

病毒衣壳的力学特性与其结构内的局部构象动力学存在紧密关联。其不仅可反映病毒衣壳抵御基因组装载过程中产生的超高内部压力所必需的结构稳定性，还能助力病毒感染周期内衣壳成熟、基因组脱壳与受体结合等关键事件的顺利完成。
生物纳米颗粒的力学特性通常通过原子力显微镜（Atomic Force Microscopy, AFM）纳米压痕实验监测其动态形变来测定，但此前尚无一套能够完整覆盖所有已观测到的形变行为的综合理论。
本研究提出一种用于建模生物纳米颗粒动态形变的全新理论，该理论同时考虑了压头与颗粒物理接触引发的非线性赫兹（Hertzian）形变，以及用于模拟颗粒结构的曲元（梁）的弯曲形变。当梁的形变突破临界阈值时，会触发颗粒向塌陷状态的动态转变，这一极端现象会伴随实验或模拟所得力（F）-形变（X）谱中观测到的灾难性力骤降。
该理论可借助赫兹形变与弯曲形变对应的杨氏模量（Young’s moduli），以及依赖结构损伤的梁存活概率（以最大强度与协同性参数表征），解析力-形变曲线中的各类精细特征，包括其非线性组分。
本研究通过将理论曲线与多种病毒颗粒的实验力-形变谱进行对比，成功验证了该理论对天然纳米颗粒形变动力学的描述能力。该方法可为生物与人工纳米颗粒的动态结构转变提供全面阐释，这对于其在纳米技术与纳米医学领域的优化应用至关重要。